The derivation of the equilibrium equations of bending and torsion of a thin-walled rod with an arbitrary contour of the cross section is given. The structural elements of the rod, represented by longeron and stringer belts, have tensile–compressive rigidity, and the panels perceive only shear. Panels connect the belts, which ensures joint deformation of all elements of the rod. The movement of the belts is determined by the hypothesis of flat sections. With tight torsion, the movements of the belts depend on the geometric parameters and may not coincide with the plane of the cross section. Only the torque acts on the rod, in this case, the internal forces in the belts satisfy the equations: the sum of the forces and the sum of the bending moments are zero. The rank of the matrix of equations is three, therefore, it is proposed in the work to form groups with a different number of belts, and for each of them to form equilibrium equations for the constrained torsion of a thin-walled rod. This is a peculiar form of belt equilibrium equations. Examples of rod’s torsion are considered.

中文翻译：

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薄壁杆的弯曲和扭曲扭力

给出了具有任意横截面轮廓的薄壁杆的弯曲和扭转平衡方程的推导。杆的结构元素以纵长带和纵梁带为代表，具有抗拉刚度，面板只能承受剪切力。面板连接皮带，以确保杆上所有元件的共同变形。皮带的运动取决于平面截面的假设。在紧密扭转的情况下，皮带的运动取决于几何参数，并且可能与横截面的平面不一致。仅扭矩作用在杆上，在这种情况下，皮带中的内力满足以下公式：力的总和和弯矩的总和为零。方程矩阵的等级为三，因此，在工作中，建议形成具有不同数量皮带的组，并为每个皮带形成平衡方程，以约束薄壁杆的扭转。这是皮带平衡方程的一种特殊形式。考虑杆的扭转的例子。